Transcript The student - Nuova Direzione Didattica Vasto

Mathematics
curriculum
in Poland
Overview : fourth to sixth
classes
Aims
Broad objectives:
Calculating skills
Students make simple memory operations: addition, substraction,
multiplication,division using the positive integers (whole numbers), integers and
fractions. They know and use algorithms to make calculations. Students can use
acquired concepts, skills and processes in real problem-solving situations.
Making and using mathematical information
Students interpret text, number and graphical information. They know the basic
mathematical concepts and are able to explain the meaning of them. Students
formulate answers and write the results in a correct way.
Mathematical modelling
Students adjust correct mathematical formulae to simple situations. Students
explore, perceive, use and appreciate mathematical patterns in order to convert the
text of the exercise into simple, arithmetic equation.
Understanding and making of strategies
Students use acquired simple concepts, establish the sequence of doings (including
calculations) in the process of problem-solving. Students plan, monitor and evaluate
solutions.They can also draw conclusions using different kind of information and
facts provided or learnt.
The content of teaching- strands
The positive integers in decimal system.
The student :

reads and writes the multi-digit integers (whole numbers)

interprets the integers on a number line

compares the integers
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round whole numbers e.g round whole numbers to nearest ten, hundred, thousand

changes decimals up to 30 into Roman numerals and vice versa
Whole number calculations
The student:

explores and identifies place value in whole numbers

adds and substracts multi-digit numbers and solves simple problems

knows and recalls addition and subtraction facts

solves word problems involving addition and subtraction

develops an understanding of multiplication as repeated addition and vice versa.

adds and subtracts whole numbers without and with a calculator

multiplies and divides integres by other whole numbers, without and with a calculator

identifies whole numbers divided by 2, 3, 5, 9, 10, 100

identifies and explores square and cube roots

divides two-digit numbers into prime factors
The content of teaching- strands
Directed numbers
The student:
1.
identifies positive and negative numbers in context
2.
identifies positive and negative numbers on the number line
3.
calculates the absolute value
4.
compares directed numbers
5.
makes simple memory calculations usind directed numbers
Fractions and decimal fractions
The student:
1.
calculates a unit fraction of a number and calculates a number, given a unit fraction of the number
2.
reduces or simplifies the fractions
3.
finds common denominator to fractions
4.
expresses improper fractions as mixed numbers and vice versa
5.
rounds decimal fractions
6.
adds and subtracts simple fractions and simple mixed numbers
7.
compares and orders fractions and decimals
8.
multiplies a fraction by a whole number and a fraction by a fraction
9.
expresses tenths, hundredths and thousandths in both fractional and decimal form
Fraction and decimal fraction calculations
The student:
1.
adds and subtracts whole numbers and decimals without and with a calculator
2.
multiplies and divides a decimal by a whole number, without and with a calculator
3.
makes simple calculations using fractions and decimal fractions
4.
estimates the results of calculations
5.
compares fractions differentially
6.
identifies and explores square roots and cube roots of fractions
7.
computes the integer fraction
The content of teaching- strands
Elements of Algebra
The student:
1.
2.
3.
identifies positive and negative numbers in context
identifies positive and negative numbers on the
number line
adds simple positive and negative numbers on the
number line
The content of teaching- strands
Straight lines and sections (lenghts)
The student:
1. identifies, describes figures: point, straight ,ray, length
2. identifies, describes and classifies vertical, horizontal and parallel lines
3. identifies, describes and classifies oblique and perpendicular lines
4. measures the length with an accuracy of 1 millimeter
5. knows if he wants to find the distance from a point to a line he must find the
length of the perpendicular line
Angles
The student:
1. recognises, classifies and describes angles, their rays and vertex
2. measures angles less than 180 degrees with accuracy of 1 degree
3. draws an angle less than 180 degrees
4. classifies angles as acute, obtuse and right angles
5. estimates angle sizes
6. recognises and uses features of apex and adjacent angles
The content of teaching- strands
2-D shapes
The student:
1. classifies and describes triangles and quadrilaterals
2. identifies, describes and classify 2-D shapes: equilateral, isosceles and
scalene triangle, rectangle, parallelogram, rhombus, trapesoid
3. explores, describes and compares the properties (sides, angles, parallel
and non-parallel lines) of 2-D shapes
4. identifies the properties of the circle: diameter, radius and chord circle
5. uses the assertion of the sum of angles in a triangle
3-D shapes
The student:
1. identifies, describes and classifies 3-D shapes, including cube, cuboid,
cylinder, cone, sphere, triangular prism, pyramid
2. recognises the nets of prisms and pyramids
3. draws the nets of simple 3-D shapes (prisms)
The content of teaching- strands
Calculating area, length, and other geometric properties
The student:
1.
2.
3.
4.
5.
6.
calculates the perimeter a polygon
calculates the area of the square, rhombus, parallelogram, triangle and
trapezium presented on a drawing and in practical situations
estimates and measures length using appropriate metric units
calculates area using acres and hectares
estimates and measures capacity using appropriate metric units
calculates angle measures
The content of teaching- strands
Practical calculations
The student:
1.
2.
3.
4.
5.
6.
7.
develops an understanding of simple percentages and relate them to
fractions and decimals
solves problems involving operations with whole numbers, fractions,
decimals and simple percentages
solves and completes practical tasks and problems involving times and
dates
reads the temperature on the Celsius scale
renames the measures of weight and length
identifies given scale and draws items to a larger or smaller scale.
in the practical situation calculates the length of the road at a given
speed and given time and so forth
The content of teaching- strands
Elements of mathematical statistics
The student:
1. compiles and uses simple data sets
2. uses charts, graphs and tables to read and interpret data
Problem-solving activities
The student:
1. reads with understanding a simple text which includes number information
2. can extract important information and data from the activity, makes auxiliary
drafts before solving the operation
3. notices the relationship between the information and data provided
4. selects appropriate concepts, methods and techniques to apply to mathematical
problems.
5. makes connections and begins to reason deductively in geometry, number and
algebra, including using geometrical constructions
6. verifies the outcome of the execise, judging its meaningfulness